A professor writes N consecutive natural numbers, beginning with 1, on the blackboard. One of the students in the class deletes one of the numbers (exactly one number), from that list.
Now, given that the average of the remaining N-1 numbers is 271/16.
Can you find out the number that has been deleted from the list ?

Well that number is close to 17, but the sum of numbers through 17 is 153, so the numerator is way too large at 271/16. Moreover, if the average is 17, then there must be 33 numbers. Therefore, double that number, and you have 542/32. Now, if N=33, the sum comes to 561, and 561/33 = 17, so we are missing the number 561-542=19. Answer is 19.

Posted by Lawrence on 2003-08-28 02:38:18